lec15 - CSE20 Lecture 15 Karnaugh Maps Professor CK Cheng...

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CSE20 Lecture 15 Karnaugh Maps Professor CK Cheng CSE Dept. UC San Diego 1
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Example Given F = Σ m (3, 5), D = Σ m (0, 4) 0 2 6 4 1 3 7 5 b c a - 0 0 - 0 1 0 1 Primes: Σ m (3), Σ m (4, 5) Essential Primes: Σ m (3), Σ m (4, 5) Min exp: f(a,b,c) = a’bc + ab’ 2
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Boolean Expression K-Map Variable x i and its compliment x i Two half planes Rx i , and Rx i Product term P ( Π x i * e.g. b’c’) Intersect of Rx i * for all i in P e.g. Rb’ intersect Rc’ Each minterm One element cell Two minterms are adjacent iff they differ by one and only one variable, eg: abc’d, abc’d’ The two cells are neighbors Each minterm has n adjacent minterms Each cell has n neighbors 3
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Procedure Input: Two sets of F  R  D 1) Draw K-map. 2) Expand all terms in F to their largest sizes (prime implicants). 3) Choose the essential prime implicants. 4) Try all combinations to find the minimal sum of products. (This is the most difficult step) 4
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Example Given F = Σ m (0, 1, 2, 8, 14) D = Σ m (9, 10) 1. Draw K-map 0 4 12 8 1 5 13 9 3 7 15 11 2 6 14 10 b c a d 1 0 0 1 1 0 0 - 0 0 0 0 1 0 1 - 5
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2. Prime Implicants: Largest rectangles that intersect On Set but
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lec15 - CSE20 Lecture 15 Karnaugh Maps Professor CK Cheng...

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